Electromagnetic scattering from anisotropic materials, part I: General theory

Integro-differential equations are obtained for the electric and magnetic fields inside a linear, lossy, and anisotropic scatterer, in the frequency domain. The material of the scatterer is characterized by arbitrary values of the elements of the relative permittivity tensor
\bar{\epsilon}
, the relative permeability tensor
\bar{\mu}
, and the conductivity tensor
\bar{\sigma}
. The results are specialized to the case of oblique scattering in two dimensions, for which a numerically efficient computer code has been developed and tested, as described in a companion paper (Part II). The method developed herein is based on a comparison between macroscopic and microscopic descriptions of electromagnetic fields in material media, and is of general applicability.